Among the widely-used instruments for measuring surface topographies are interferometers, which utilize the wave nature of light to map variations in surface height with high accuracy. However, it is well understood that if the source light for the interferometer is essential monochromatic--that is, characterized by a single-color emission having no perceptible spectral width in normal use of the instrument--it is not generally possible to accurately measure surface features with discontinuous height variations or surface roughness that exceed one-quarter of the wavelength of the source light. Such surface features result in interferometric phase ambiguities that are difficult or impossible to interpret. For this reason, a variety of instruments that are based on spectrally broadband or multiple-color sources have been proposed in an effort to overcome this limitation. The present invention relates to this form of instrument and to methods incorporating such instruments.
It is well known that white-light and multiple-color interferometers can overcome the problems associated with phase ambiguities, and these instruments are very useful for high-precision length measurement and surface profiling. For example, the colors seen in white-light interference patterns, first described by Hooke in 1665, are a sensitive measure of thickness between reflecting surfaces. In 1893, A. A. Michelson used white light to estimate the size of a series of step-shaped etaIons as part of the procedure leading to the first comparison of the wavelength of light with the International Prototype Meter (12 Astronomy and Astro-Physics, pp. 558-60). Many of the traditional optical instruments for calibrating gauge blocks, which employ white light or multiple-color sources, as well as special microscopes suitable for white-light interferometry, have been available commercially for a number of years. White-light interference microscopes have been widely used for measuring film thicknesses and for monitoring surfaces with discontinuities several wavelengths deep.
The underlying principles of single- and multiple-color interferometry, as well as the use of white-light fringes to determine an optical path difference (OPD), are extensively treated in elementary optics texts. For example, the book Physical Optics by Robert W. Wood, first published in 1905 and recently reprinted by the Optical Society of America (Washington, D.C., 1988), provides numerous and detailed descriptions of phenomena related to white-light fringes, the interference colors in thin films, testing of optical components, measurement of phase-change on reflection using Newton's rings, dissonance and consonance of interference fringes formed in two-color sodium light, and the determination of lengths, gaps and film thicknesses by interferometry.
Although the basic principles of white-light and multiple-color interferometry are fundamental concepts of optics, the practical implementation of these principles in automated instruments is a fairly recent development. A detailed description of an automated white-light thickness gauge for plane-parallel films appears in an article by P. A. Floumoy, R. W. McClure and G. Wyntjes entitled White Light Interferometric Thickness Gauge, 11 Appl. Opt. 1907-15 (1972). The disclosed instrument is capable of measuring thicknesses from 2.5 to 500 .mu.m with a resolution of 0.05 .mu.m using mechanically-scanned interferometer mirrors and electronic intensity detection. Another implementation of a white-light interferometer is described by R. C. Youngquist, S. Carr and D. E. N. Davies in Optical Coherence-Domain Reflectometry: A New Optical Evaluation Technique, 12 Opt. Let. 158-60 (1987). That system is designed to determine positions and magnitudes of reflection sites within miniature optical assembles by searching for positions of high fringe contrast.
White-light (i.e. low coherence) interferometry for the analysis of optical waveguides has also been developed. Some of the known methods involve analyzing one-dimensional interferograms for their spatial frequency content using Fourier transform techniques. For example, in an article by A. Kohlhass, C. Froemchen and E. Brinkmeyer, High-Resolution OCDR For Testing Integrated-Optical Waveguides: Dispersion-Corrupted Experimental Data Corrected By A Numerical Algorithm, 9 J. Lightwave Tech. 1493-1502 (1991), there is presented a Fourier-transform technique for correcting dispersion-corrupted interferograms from integrated-optical waveguides. Similarly, an article by B. L. Danielson and C. Y. Boisrobert, Absolute Optical Ranging Using Low Coherence Interferometry, 30 Appl. Opt. 2975-79 (1991) describes a fiber-optic instrument evaluated as part of a program to develop diagnostic probes for testing the guiding characteristics of semiconductor laser sources. The article emphasizes the advantages of processing the data in the spatial frequency domain for absolute optical ranging through dispersive transparent media.
Despite the advances that have been made in the application of white-light interferometry to one-dimensional distance measurement, relatively few methods for obtaining three-dimensional representations of surface topography are known in the art. All such known methods are based on analysis of fringe contrast. Briefly described, the physical principles underlying the conventional fringe contrast method for topographical measurement are as follows. A typical white-light interferogram can be approximated by a constant bias I.sub.DC and a series of sinusoidal interference fringes modulated by an envelope function V: EQU I=I.sub.DC +V.multidot.sin(.phi.). (Equation 1)
The envelope function V is the fringe contrast, which varies much more slowly with changes in the OPD than the fringe phase .phi.. The term fringe contrast has many synonyms such, for example, as fringe visibility, modulation, signal variance, modulus of the complex degree of coherence, and so on, depending upon the context of its use. It is a basic principle of optics that the peak contrast for white-light fringes in an ideal, dispersion-compensated interferometer occurs when the OPD is zero. Accordingly, a known technique for measuring surface topography is the determination of the position of maximum contrast simultaneously for a plurality of points on the surface being profiled, using an interferometer equipped with mechanical means for varying the OPD.
The first practical method and apparatus for automated, three-dimensional measurement of surface topography using white-light interferometry was disclosed in U.S. Pat. No. 4,340,306 to Balasubramanian, which issued Jul. 20, 1982. That patent describes a white-light interferometer which includes a mechanically-scanned reference mirror, a two-dimensional detector array, and computer control. The object and reference wavefronts are imaged together onto the detector array so that each detector element (pixel) corresponds to a point or location on the object surface. The method involves varying the OPD by scanning either the reference mirror or the object in discrete steps, measuring the fringe contrast for each pixel at each scan position, and in this manner determining for each surface point the position of maximum fringe contrast. The scan position for which the contrast is a maximum is a measure of the relative height of a particular surface point. An important feature introduced by Balasubramanian relates to the efficient use of computer memory. Although a great number of data points are processed in order to achieve a full three-dimensional image, the data acquisition method processes the data in a dynamic fashion so that very few computer registers are required for each pixel. At each point in the scan, the current fringe contrast for each pixel is compared to a stored value and, if it is larger, it replaces the stored value for that pixel, together with the current scan position. If the current fringe contrast is less than the stored value, on the other hand, it is discarded. This procedure dramatically reduces the memory requirements of the computer.
White-light interferometric microscopes are particularly useful for sectioning images according to surface height, in a manner analogous to confocal microscopes but without the complexity and high cost of confocal instruments. The application of automated mechanical scanning and detection of peak fringe contrast to the profiling of microscopic objects such as integrated circuits and the like is disclosed in U.S. Pat. No. 4,818,110 to Davidson. The apparatus is based on a common Linnik interference microscope, with the addition of electronic means for the processing of video images to obtain fringe contrast information and a piezoelectric transducer (PZT)-actuated object stage controlled by a computer. Similarly, in an article by B. S. Lee and T. C. Strand, Profilometry With A Coherence Scanning Microscope, 29 Appl. Opt. 3784-88 (1990), it is shown that white-light interferometry can improve lateral resolution over conventional microscopes, in addition to providing information about surface topography.
There have been many improvements related to rapid determination of fringe contrast in white-light interferometers and to the reduction of data to representations of three-dimensional images. An article by T. Dresel, G. Haeusler and H. Venzke entitled Three-Dimensional Sensing Of Rough Surfaces By Coherence Radar, 31 Applied Optics 919-25 (1992), describes an interferometer for rough surfaces metrology and comprised of a broadband source, a two-dimensional detector array, a reference mirror actuated by a PZT, and a mechanical translation stage for scanning the object. For each scan position, three intensity images are taken of the interferometer's output, corresponding to three different phases of the reference wave separated by 22.pi./3 radians. The three phase shifts are obtained by small displacements of the reference mirror. The three intensity values per scan position are used in a simple formula to calculate the fringe contrast for each image pixel. At each position in the scan, the current fringe contrast for each pixel is compared to a stored valued and, if the current contrast value is larger, it replaces the stored value for that pixel, together with the current scan position. Several figures in the article depict graphical images of three-dimensional objects, including those considered rough according to the standards of conventional interferometry.
Another technique for rapidly measuring fringe contrast is by digitally filtering the interference data. In an article by Stanley S. C. Chim and G. S. Kino, Three-Dimensional Image Realization In Interference Microscopy, 31 Appl. Opt. 2550-53 (1992), there is described a digital filter algorithm for rapidly extracting the fringe contrast envelope. The interferograms are obtained by scanning an object through discrete positions separated by approximately 50 nm. After subtracting an estimate of I.sub.DC from the data, the results are passed through a known form of digital filter to recover the envelope which is then analyzed to determine the position of peak fringe contrast.
U.S. Pat. No. 5,133,601 to Cohen et al describes a white-light interference microscope equipped with a video camera and a PZT attached to effect mechanical scanning of the OPD. At each point in the scan, the current fringe contrast for each pixel is compared to a stored value and, if the current value is larger, it replaces the stored value for that pixel, together with the current scan position. Three methods for measuring the fringe contrast are there presented. The first calculates the fringe contrast at each scan position using five equally-spaced points on an interference fringe. The second uses three points to calculate fringe-contrast and combines the result with the mean interferometric phase for improving resolution. In the third method, a succession of image frames of intensity data are taken during a mechanical scan, the distance between frames being 50 nm . After subtracting an estimate of I.sub.DC from the data, the results are passed through a known form of digital filter to recover the envelope.
It is noteworthy that in all of the above-mentioned references, and in numerous other articles and patents related to measuring surface topography with white-light interferometry, surface height is determined by a systematic search to locate the maximum fringe contrast for each image pixel during a mechanical scan. Thus, all prior art methods for measuring surface topography with white-light interferometry are based on some variation of Equation 1. The data processing invariably consists of determining the position of maximum fringe contrast for a plurality of points on the object surface as imaged onto a detector array.
Using the position of maximum fringe contrast to topographically map surface features has many fundamental disadvantages. The contrast method requires a great number of calculations, but most of the results are discarded, and very few or only one data point per pixel is preserved for the final measurement. Thus the method does not make effective use of all of the available interference data. In addition, the method is unusually sensitive to random noise, such as spikes or missing data points, that would be interpreted as positions of high fringe contrast.
A further disadvantage of most fringe-contrast calculation techniques is that they are highly wavelength dependent and may fail if the mean wavelength or other spectral properties of the source vary due to changes in environmental conditions or adjustments to illumination strength. Generally, the fringe contrast envelope must be assumed to be of a particular functional form, such as Gaussian, in order to be accurate; distortions of the envelope shape due to surface colors or unexpected or unusual source spectra can also lead to significant errors.
Still another disadvantage of fringe-contrast methods characteristic of the prior art is that the object or reference wavefront must be displaced according to particular fixed distance intervals, and no procedure is provided for adjusting the density of data points per interference fringe to optimize the signal-to-noise ratio and data acquisition speed in accordance with surface characteristics and desired precision. In particular, all automated white light interferometers presently known in the art require a minimum of two data points per interference fringe (i.e. the Nyquist rate), and often require five or more points spaced at precise intervals. This minimum sampling rate severely limits the speed at which topographical images can be acquired and processed.
Finally, it is noted that a serious and fundamental limitation of the fringe-contrast method is that the correspondence between maximum fringe contrast and zero OPD holds true only for ideal interferometers that have been perfectly compensated for chromatic dispersion. Thus, if the interferometer is imperfect, or the object is composed of a transparent, dispersive medium, then the fringe contrast envelope is shifted with respect to the zero OPD position and may be severely distorted. Under these conditions, it is not possible to obtain accurate three-dimensional images using any known prior art white-light method or apparatus.